Question

Spam filters try to sort your​ e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming​ e-mail and assigns points to the​ sender, the​ subject, key words in the​ message, and so on. The higher the point total the more likely it is that the message is unwanted. The filter has a cutoff value for the point​ total; any message rated lower than that cutoff passes through your​ inbox, and the​ rest, suspected to be​ spam, are diverted to the junk mailbox. We can think of the​ filter's decision as a hypothesis test. The null hypothesis is that the​ e-mail is a real message and should go in your inbox. A higher point total provides evidence that the message may be​ spam; when​ there's sufficient​ evidence, the filter rejects the​ null, classifying the message as junk. This usually works pretty​ well, but, of​ course, sometimes the filter makes a mistake. Complete parts​ (a) through​ (c) below.

1. In this​ context, what is meant by the power of the​ test?

A. Power is the probability the filter does not detect a real message that should go to your inbox.

B. Power is the probability the filter does not detect spam.

C. Power is the probability the filter detects spam.

D. Power is the probability the filter detects a real message that should go to your inbox.

​2. What could you do to increase the​ filter's power?

A. To increase​ power, add more components for the filter to check.

B. To increase​ power, filter the​ e-mails manually.

C. To increase​ power, lower the cutoff value.

D. To increase​ power, raise the cutoff value.

3. What is the disadvantage of taking the action in part​ (b)?

A. There would be a higher risk of Type I and Type II errors.

B. More real messages would end up in your junk mailbox.

C. More spam would end up in your inbox.

D. There would be a higher risk of Type II​ errors, but a lower risk of Type I errors.

Answer 1

1.  In this​ context, the power of the​ test means:

C. Power is the probability the filter detects spam.

2. To increase the​ filter's power

D. To increase​ power, lower the cutoff value.

3. The disadvantage of taking the action in part​ (b):

B. More real messages would end up in your junk mailbox.